Question
The diagram shows two sides of a parallelogram ABCD.
Find the coordinates of point D.
▶️ Answer/Explanation
Solution
Ans: (–3, 7)
Question
The diagram shows the graph of \(y = (x + 1)^2\) for \(-4 \leq x \leq 2\)
(a) On the same grid, draw the line \(y = 3\)
(b) Use your graph to find the solutions of \((x + 1)^2 = 3\).
Give each solution correct to 1 decimal place.
▶️ Answer/Explanation
Solution
(a)
The line \(y = 3\) is a horizontal line intersecting the y-axis at 3.
(b) Ans: \(x = 0.7\) and \(x = -2.7\) (1 d.p.)
From the graph, the solutions are the x-coordinates where \(y = (x + 1)^2\) intersects \(y = 3\).
Algebraically, \((x + 1)^2 = 3\) leads to \(x + 1 = \pm \sqrt{3}\).
Thus, \(x = -1 \pm \sqrt{3} \approx -1 \pm 1.732\).
Solutions: \(x \approx 0.7\) and \(x \approx -2.7\) (correct to 1 decimal place).